document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115300>Question 115300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small lake is stocked with a certain species of fish. The fish population is modeled by the function <BR>\n" );
document.write( "P=10/1+4e^-0.8t \r<BR>\n" );
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document.write( "where, P is the number of fish in thousands and t is measured in years since the lake was stocked. \r<BR>\n" );
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document.write( "The fish population (correct up to two decimal places) after 3 years is______  <BR>\n" );
document.write( "(Remark: don't forget to use the correct units for P .) \r<BR>\n" );
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document.write( "The fish population reaches 5000 after  years is __________ (correct up to two decimal places). <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84091 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A small lake is stocked with a certain species of fish. The fish population is modeled by the function<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E%28-0.8t%29%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E%28-0.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where, P is the number of fish in thousands and t is measured in years since the lake was stocked.<BR>\n" );
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document.write( "The fish population (correct up to two decimal places) after 3 years is______<BR>\n" );
document.write( "(Remark: don't forget to use the correct units for P .)<BR>\n" );
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document.write( "Substitute 3 for t in the given equation:<BR>\n" );
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document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E%28-0.8%2A3%29%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E%28-0.8%2A3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E-2.4%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E-2.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find e^-2.4 on a good calc:<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4%2A.0907%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4%2A.0907%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F1.623 ALIGN=MIDDLE  ALT=\"10%2F1.623\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = 7.34 thousand <BR>\n" );
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document.write( "The fish population reaches 5000 after years is __________ (correct up to two decimal places).<BR>\n" );
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document.write( "P = 5<BR>\n" );
document.write( "5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E%28-0.8t%29%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E%28-0.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ";<BR>\n" );
document.write( "Multiply both sides by = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4e%5E%28-0.8t%29%29 ALIGN=MIDDLE  ALT=\"%281%2B4e%5E%28-0.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "5<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4e%5E%28-0.8t%29%29 ALIGN=MIDDLE  ALT=\"%281%2B4e%5E%28-0.8t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10<BR>\n" );
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document.write( "Divide both sides by 5:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B4e%5E%28-0.8t%29 ALIGN=MIDDLE  ALT=\"1%2B4e%5E%28-0.8t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
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document.write( "Subtract 1 from both sides and you have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4e%5E%28-0.8t%29 ALIGN=MIDDLE  ALT=\"4e%5E%28-0.8t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Divide both sides by 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-0.8t%29 ALIGN=MIDDLE  ALT=\"e%5E%28-0.8t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .25\r<BR>\n" );
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document.write( "-.8t = ln(.25); remember the ln(e) = 1<BR>\n" );
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document.write( "-.8t = -1.3863<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1.3863%29%2F%28-.8%29 ALIGN=MIDDLE  ALT=\"%28-1.3863%29%2F%28-.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 1.733 years<BR>\n" );
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document.write( "Check solution by using 1.73 for t in the original equation and find P<BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E%28-0.8%2A1.73%29%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E%28-0.8%2A1.73%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4e%5E-1.3863%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4e%5E-1.3863%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B4%2A.25%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B4%2A.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%281%2B1%29 ALIGN=MIDDLE  ALT=\"10%2F%281%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P = 5 which is 5000 fish   </SPAN>\n" );
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